Strings on the back. One neck, or two back to back?

Something Ted said made me think it might be possible to put 10 or 12 strings on the back of an existing 10 string instrument's neck. I thought I absolutely had to have two necks back to back and with trusses. Maybe that's ideal but not absolutely required. What do you think? Can I get away with only one neck? What would be the best way of doing that?

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Here's the issue with two necks back to back. Added thickness. See the blueprint here. It's an older design I drew that was just going to put two 2 string basses on the back of an existing Chapman Stick skirting by the belthook. My idea now is to remove/redesign the belthook and have strings covering the whole back of the instrument. The belthook would come out of the sides instead.